Understanding the Expression
To solve the expression \( 6 \times \frac{3}{4} - 2 \times \frac{1}{3} \), we will break it down into simpler steps.

Step 1: Evaluate Each Term
- **First Term: \( 6 \times \frac{3}{4} \)**
- Multiply \( 6 \) by \( \frac{3}{4} \):
- \( 6 \times \frac{3}{4} = \frac{6 \times 3}{4} = \frac{18}{4} \)
- Simplifying \( \frac{18}{4} \) gives \( \frac{9}{2} \) or \( 4.5 \).
- **Second Term: \( 2 \times \frac{1}{3} \)**
- Multiply \( 2 \) by \( \frac{1}{3} \):
- \( 2 \times \frac{1}{3} = \frac{2 \times 1}{3} = \frac{2}{3} \)

Step 2: Convert to a Common Denominator
To subtract \( \frac{9}{2} \) and \( \frac{2}{3} \), we need a common denominator. The least common multiple (LCM) of \( 2 \) and \( 3 \) is \( 6 \).
- **Convert \( \frac{9}{2} \) to Sixth:**
- \( \frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6} \)
- **Convert \( \frac{2}{3} \) to Sixth:**
- \( \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)

Step 3: Perform the Subtraction
Now we can subtract:
- \( \frac{27}{6} - \frac{4}{6} = \frac{27 - 4}{6} = \frac{23}{6} \)

Final Answer
The result of \( 6 \times \frac{3}{4} - 2 \times \frac{1}{3} \) is \( \frac{23}{6} \) or approximately \( 3.83 \).